Devices are known for making the composite tape structure described above. Such devices are described in U.S. Pat. Nos. 4,582,737 and 4,415,400. The device described in U.S. Pat. No. 4,582,737, however, forms rolls of the composite tape structure for later use to mask a surface, in which rolls the exposed portions of the layers of adhesive along the edges of the composite tape can not be firmly releasably adhered to an adjacent wrap of the composite in the roll because of the greater thickness of the composite along its central portion, and thus are unduly exposed to contamination and deleterious effects of the atmosphere; whereas the device described in U.S. Pat. No 4,415,400, while being able to form the composite at the location at which it is to be used, is quite complex and does not easily lend itself to forming the composite as it is being applied to a surface to be masked.